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lm.Rd
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lm.Rd
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\name{lm}
\title{Fitting Linear Models}
\usage{
lm(formula, data, subset, weights, na.action,
method = "qr", model = TRUE, x = FALSE, y = FALSE, qr = TRUE,
singular.ok = TRUE contrasts = NULL, offset = NULL, \dots)
lm.fit (x, y, offset = NULL, method = "qr", tol = 1e-7, \dots)
lm.wfit(x, y, w, offset = NULL, method = "qr", tol = 1e-7, \dots)
lm.fit.null (x, y, method = "qr", tol = 1e-7, \dots)
lm.wfit.null(x, y, w, method = "qr", tol = 1e-7, \dots)
}
\alias{lm}
\alias{lm.fit}
\alias{lm.wfit}
\alias{lm.fit.null}
\alias{lm.wfit.null}
\arguments{
\item{formula}{a symbolic description of the model to be fit.
The details of model specification are given below.}
\item{data}{an optional data frame containing the variables
in the model. By default the variables are taken from
the environment which \code{lm} is called from.}
\item{subset}{an optional vector specifying a subset of observations
to be used in the fitting process.}
\item{weights}{an optional vector of weights to be used
in the fitting process. If specified, weighted least squares is used
with weights \code{weights} (that is, minimizing \code{sum(w*e^2)});
otherwise ordinary least squares is used.}
\item{na.action}{a function which indicates what should happen
when the data contain \code{NA}s. The default is set by
the \code{na.action} setting of \code{\link{options}}, and is
\code{\link{na.fail}} if that is unset. The ``factory-fresh''
default is \code{\link{na.omit}}.}
\item{model, x, y, qr}{logicals. If \code{TRUE} the corresponding
components of the fit (the model frame, the model matrix, the
response, the QR decomposition) are returned.}
\item{singular.ok}{logical, defaulting to
\code{TRUE}. \emph{\code{FALSE} is not yet implemented}.}
\item{method}{currently, only \code{method="qr"} is supported.}
\item{contrasts}{an optional list. See the \code{contrasts.arg}
of \code{model.matrix.default}.}
\item{offset}{this can be used to specify an \emph{a priori}
known component to be included in the linear predictor
during fitting. An \code{\link{offset}} term can be included in the
formula instead or as well, and if both are specified their sum is used.}
\item{tol}{tolerance for the \code{\link{qr}} decomposition. Default
is 1e-7.}
\item{\dots}{currently disregarded.}
}
\description{
\code{lm} is used to fit linear models.
It can be used to carry out regression,
single stratum analysis of variance and
analysis of covariance (although \code{aov} may provide a more
convenient interface for these).
}
\details{
Models for \code{lm} are specified symbolically. A typical model has
the form \code{response ~ terms} where \code{response} is the (numeric)
response vector and \code{terms} is a series of terms which specifies a
linear predictor for \code{response}. A terms specification of the form
\code{first+second} indicates all the terms in \code{first} together
with all the terms in \code{second} with duplicates removed. A
specification of the form \code{first:second} indicates the the set of
terms obtained by taking the interactions of all terms in \code{first}
with all terms in \code{second}. The specification \code{first*second}
indicates the \emph{cross} of \code{first} and \code{second}. This is
the same as \code{first+second+first:second}.
}
\value{
\code{lm} returns an object of \code{\link{class}} \code{"lm"}.
The functions \code{summary} and \code{\link{anova}} are used to
obtain and print a summary and analysis of variance table of the results.
The generic accessor functions \code{coefficients},
\code{effects}, \code{fitted.values} and \code{residuals}
extract various useful features of the value returned by \code{lm}.
}
\seealso{
\code{\link{summary.lm}} for summaries and \code{\link{anova.lm}} for
the ANOVA table. \code{\link{aov}} for a different interface.
The generic functions \code{\link{coefficients}}, \code{\link{effects}},
\code{\link{residuals}}, \code{\link{fitted.values}};
\code{\link{lm.influence}} for regression diagnostics, and
\code{\link{glm}} for \bold{generalized} linear models.
}
\note{
Offsets specified by \code{offset} will not be included in predictions
by \code{\link{predict.lm}}, whereas those specified by an offset term
in the formula will be.
}
\examples{
## Annette Dobson (1990) "An Introduction to Generalized Linear Models".
## Page 9: Plant Weight Data.
ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
group <- gl(2,10,20, labels=c("Ctl","Trt"))
weight <- c(ctl, trt)
anova(lm.D9 <- lm(weight ~ group))
summary(lm.D90 <- lm(weight ~ group - 1))# omitting intercept
summary(resid(lm.D9) - resid(lm.D90)) #- residuals almost identical
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(lm.D9, las = 1) # Residuals, Fitted, ...
par(opar)
}
\keyword{regression}